a1={a1+(1/4)}^2
a1=1/4

Sn={an+(1/4)}^2
an=Sn-S(n-1)={an+(1/4)}^2-{a(n-1)+(1/4)}^2
an=(an)^2-{a(n-1)}^2+(1/2){an-a(n-1)}
(an)^2-{a(n-1)}^2-(1/2){an+a(n-1)}=0
{an+a(n-1)}{an-a(n-1)-(1/2)}=0
an はすべて正だから an=a(n-1)+1/2